Linear and Quadratic Inequalities in One Variable [復制鏈接]

14. the sum S of the first n terms of the sequence 1, 5, 9, 13, ..., is given by the formula S=n(2n-1).

If S is greater than 435,

a. find the range of values of n.

b. what is the smallest value of n?



16. Two cars A and B travel in the same direction. After t minutes, they are at distance t(2t+30)/100 km and (t+30) km away from the starting point of car A respectively.

a. Which car takes the lead at the beginning and by what distance?

b. Which car will take the lead after exactly 40 minutes?

c. Find the range of values of t for which the leading car in (b) is overtaken by the other car.

13a.
height= [x^2-(0.5x)^2]^0.5 =0.866x
Area = x (0.866x) (0.5) = 0.433 x^2

OR

Area= 1/2 (x) (x) (sin60degree)=0.433x^2

13b.

60<0.433x^2<120
11.8<x<16.6

14. the sum S of the first n terms of the sequence 1, 5, 9, 13, ..., is given by the formula S=n(2n-1).

If S is greater than 435,

a. find the range of values of n.

b. what is the smallest value of n?

==========================================

a. 435>n(2n-1)
2n^2-n-435<0
(n-15) (2n+29)<0

n>15

b. the smallest value of n is 16

15a. Area ABCD = (12x12) - 4(1/2) (x) (12-X)
                = 2x^2 - 24x + 144

15b. 2x^2 - 24x + 144 < 74
    2x^2 - 24x + 70 < 0
    x^2 - 12x + 35 < 0
    (x-7) (x-5) <0
    5 < x < 7

[ should be <= rather than only < ]

some ammendment

引用第2樓ballballfull於2006-11-20 03:28發表的“”:
14. the sum S of the first n terms of the sequence 1, 5, 9, 13, ..., is given by the formula S=n(2n-1).
If S is greater than 435,
a. find the range of values of n.
b. what is the smallest value of n?
==========================================
a. S=n(2n-1)>435
2n^2-n-435>0
(n-15) (2n+29)>0
n>15
b. the smallest value of n is 16

16. Two cars A and B travel in the same direction. After t minutes, they are at distance t(2t+30)/100 km and (t+30) km away from the starting point of car A respectively.

a. Which car takes the lead at the beginning and by what distance?

b. Which car will take the lead after exactly 40 minutes?

c. Find the range of values of t for which the leading car in (b) is overtaken by the other car.

=======================

a. At time t=0, A = 0, B = 30
Trivial result (B leads A by 30 km )

b. Sub t=40, trivial (B leads A)


c. Consider p(t)= t(2t+30)/100 - (t+30)
              = (2t^2-70t-3000) / 100

p(t) >0 when (2t^2-70t-3000)>0
i.e. t^2-35t-1500 > 0
(t-60) (t+25) >0

So p(t) >0 when t>60 (A leads B)
Therefore p(t) <0 when 0<t<60 (B leads A)

果然係神

引用第4樓kylau於2006-11-20 12:41發表的“”:
some ammendment

係喎

其實我做番呢d數
發覺我唔記得好多

不過maths mc題好玩d，又深d

引用第7樓ballballfull於2006-11-20 13:08發表的“”:
係喎
其實我做番呢d數
發覺我唔記得好多
不過maths mc題好玩d，又深d

我反而覺得paper 1 的 section b 難 (大部分考生死在此地)
識就識, 唔識就有一hour 都唔識做


mc題好玩d, 又深d, 但唔識做的, 大部分可以用sub數方法找回suitable answer (method of putting value)
我教補習, 做mc 經常會叫學生用 method of putting value 同 method of elimination

我個時考係54題mc
好似5個chice分布一定係
12,11,11,10,10
加埋54條
我做完諗住arm晒
點知錯4條

做mc玩埋技巧又有d深問題
當年想讀數學，但現在中5的也忘記了一半
pure math 就更加